Displays that can be reversibly stretched in their geometrical layout are highly important in various applications. Stretchable displays are commonly demonstrated using two-dimensional (2D) geometries with stretchable rubber substrates and elastic interconnects. However, mechanical stretch induces deterioration of the resolution per unit area and blurs the displayed image, consequently lowering the display quality. In this study, we demonstrate a morphable 3D structure inspired by origami/kirigami to produce stretchable displays that can preserve the original image quality by maintaining the display pixel density under stretching. The morphable 3D display consists of a 7 × 7 micro-light-emitting diode (LED) pixel array integrated on a transparent epoxy structural frame, which can be stretched up to 100% without affecting the performance of the display. The functional 3D system can create important unconventional opportunities for optoelectronic devices.